The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  2  1  1  X  1  1  X  1  1  2  1  1  0  1  1 X+2  1  1  1  1  0 X+2  1  1  1  1  2  X  1  1  1  1  2  X  X  X  0  X  X  2  1  1  1  1  0 X+2  1  1  1  1  2  X  X  X  0  X  X X+2  2  2  0  0  0  2  1  1  1  1  1  1  1  X
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  2 X+3  1  X  1  1  0 X+1  1 X+2  3  1  0 X+2 X+1  3  1  1  2  X X+3  1  1  1  2  X X+3  1  1  1  0 X+2  X  2  X  X  0 X+2 X+1  3  1  1  2  X X+3  1  1  1  0 X+2  X  2  X  1  0  2  X  2  0  X  0 X+2  2  X X+1  3 X+3  0
 0  0  2  2  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2  2  0  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  2  2  0  0  0  0  2  2  0  0  0  0  2  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+42x^85+32x^86+30x^87+10x^88+4x^89+2x^90+2x^93+2x^94+2x^95+1x^96

The gray image is a code over GF(2) with n=344, k=7 and d=170.
This code was found by Heurico 1.16 in 0.336 seconds.